Uniform Integrability Research Articles

Grand theories, differentiated integration

ABSTRACTEven though differentiation has become a core feature of the EU, the grand theories have focused almost exclusively on uniform integration. In this article, we derive hypotheses about differentiated integration from liberal intergovernmentalism, neofunctionalism, and postfunctionalism. In an analysis of EU treaty making between 1992 and 2016, we find evidence that heterogeneity of both wealth and identity, integration in the area of core state powers, and pre-existing differentiation drive differentiated integration. A comparison of the explanatory power of the grand theories shows that neo- and post-functionalism explain the differentiations that member states obtain in EU reform treaties more convincingly than liberal intergovernmentalism. A synthetic model performs best, however. The grand theories also leave noteworthy variation unexplained.

Minimal Root’s embeddings for general starting and target distributions

Most results regarding Skorokhod embedding problems SEP so far rely on the assumption that the corresponding stopped process is uniformly integrable, which is equivalent to the convex ordering condition Uμ≤Uν when the underlying process is a local martingale. In this paper, we study the existence, construction of Root’s solutions to SEP, in the absence of this convex ordering condition. We replace the uniform integrability condition by the minimality condition (Monroe, 1972), as the criterion of “good” solutions. A sufficient and necessary condition (in terms of local time) for minimality is given. We also discuss the optimality of such minimal solutions. These results extend the generality of the results given by Cox and Wang (2013) and Gassiat et al. (2015). At last, we extend all the results above to multi-marginal embedding problems based on the work of Cox et al. (2018).

A local Hahn–Banach theorem and its applications

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local' version of this theorem. The result is applied to study the uo-dual of a Banach lattice that was recently introduced in [3]. We also provide a simplified approach to the measure-free characterization of uniform integrability established in [8].

Some convergence properties for the maximum of partial sums of m-negatively associated random variables

In this paper, we present the Spitzer type law of large numbers for the maximum of partial sums of m-negatively associated random variables $$\left\{ X_n,n\ge 1\right\} $$ and the $$L_p$$ convergence property under the Cesaro uniform integrability condition for the maximum of partial sums. In addition, we give some simulations to verify the convergence behavior of $$\frac{1}{\psi (n)}\sum _{i=1}^{n}X_i$$ which is in accordance with our theoretical result. The main results obtained in this paper extend and improve the corresponding ones for negatively associated random variables.

Limiting behaviour for arrays of rowwise widely orthant dependent random variables under conditions of R − h-integrability and its applications

ABSTRACTIn this paper, we mainly study the convergence, complete convergence and complete moment convergence for arrays of rowwise widely orthant dependent (WOD, for short) random variables under some conditions of R-h-integrability. The results in this paper generalize and improve the corresponding ones of Sung et al., Weak laws of large numbers for arrays under a condition of uniform integrability, Journal of the Korean Mathematical Society 45 (2008), pp. 289–300, Wang and Hu, Weak laws of large numbers for arrays of dependent random variables, Stochastics: An International Journal of Probability and Stochastic Processes 86 (2014), pp. 759–775, and Wu et al., Limiting behaviour for arrays of rowwise END random variables under conditions of h-integrability, Stochastics: An International Journal of Probability and Stochastic Processes 87 (2014), pp. 409–423. As applications of the complete convergence that we established, we present some results on complete consistency for the estimator in a nonparametric regression model based on WOD errors.

Fatou's lemma for weakly converging measures under the uniform integrability condition

В статье устанавливаются лемма Фату и теорема Лебега о мажорируемой сходимости для слабо сходящихся последовательностей конечных мер и равномерно интегрируемых по этим мерам функций. Заметка содержит также новые формулировки равномерной леммы Фату, равномерной теоремы Лебега о мажорируемой сходимости, теоремы Данфорда-Петтиса и фундаментальной теоремы о мерах Янга, основанные на эквивалентности условия равномерной интегрируемости и кажущегося более слабым условия асимптотической равномерной интегрируемости для последовательностей функций и конечных мер.

The Gamma Stein equation and noncentral de Jong theorems

We study the Stein equation associated with the one-dimensional Gamma distribution, and provide novel bounds, allowing one to effectively deal with test functions supported by the whole real line. We apply our estimates to derive new quantitative results involving random variables that are non-linear functionals of random fields, namely: (i) a non-central quantitative de Jong theorem for sequences of degenerate $U$-statistics satisfying minimal uniform integrability conditions, significantly extending previous findings by de Jong (J. Multivariate Anal. 34 (1990) 275–289), Nourdin, Peccati and Reinert (Ann. Probab. 38 (2010) 1947–1985) and Dobler and Peccati (Electron. J. Probab. 22 (2017) no. 2), (ii) a new Gamma approximation bound on the Poisson space, refining previous estimates by Peccati and Thale (ALEA Lat. Am. J. Probab. Math. Stat. 10 (2013) 525–560) and (iii) new Gamma bounds on a Gaussian space, strengthening estimates by Nourdin and Peccati (Probab. Theory Related Fields 145 (2009) 75–118). As a by-product of our analysis, we also deduce a new inequality for Gamma approximations via exchangeable pairs, that is of independent interest.

Directions of arrival optimization method for broadband antenna array based on filter bank

This paper proposes an estimation method of the directions of arrival (DOA) for the broadband signals received by a uniform planar antenna array including the mutual coupling effect. The process modeling of antenna array receiving dynamic signal is obtained accurately via building the array system electromagnetic space-time model, and the mutual coupling effect is included in the synthesis procedure automatically. The broadband signal is divided into several sub-bands, and the complex weight of these sub-bands frequencies is figured out using the least mean square iteration programming. In the proposed method, the mutual coupling effect is compensated at the different frequencies. The calculation results show that the method is suitable for the uniform linear and uniform circular array pattern integration, and it is commendably satisfied with the requirement of engineering design.

Rigid double-stranded siloxane-induced high-flux carbon molecular sieve hollow fiber membranes for CO2/CH4 separation

Carbon molecular sieve (CMS) membranes are a promising candidate for natural gas processing due to their peculiar pore structure-induced excellent separation performance. Formulating ultrathin, defect-free CMS hollow fiber membranes is, however, still challenging due to damage on porous sub-structures induced by thermal relaxation of polymer chains during pyrolysis. Herein, we report a new methodology enabling high separation performance and good plasticization resistance in CMS fiber membranes by uniform integration of double-stranded polysilsesquioxanes into the polyimide matrix. Our polyimide/ladder-structured polysilsesquioxane CMS fibers substantially enhanced CO2 permeance by as much as 546% compared to the precursor fiber analogues due to the thin molecular sieve selective layer. Also, poly(dimethylsiloxane) coating delayed physical aging, still showing a high CO2 permeance of 354 GPU with CO2/CH4 selectivity of 56 after 72 days of aging. Furthermore, they exhibited excellent plasticization resistance up to a CO2 partial pressure of 13.2 bar with CO2/CH4 separation factor of 74 for an equimolar CO2/CH4 feed mixture.

Operators on Spaces of Functions and Measures. Vector Invariant (Fractal) Measures

We consider a general schema involving measure spaces, contractions and linear and continuous operators. Within the framework of this schema we use our sesquilinear uniform integral and introduce some integral operators on continuous vector function spaces, which lead us to operators on spaces of vector measures. Using these last operators, we generalize the Markov operators, obtaining via contractions vector invariant (fractal) measures. Concrete examples are provided.

Outer functions and uniform integrability

We show that, if $f$ is an outer function and $a\in[0,1)$, then the set of functions $\{\log |(f\circ\psi)^*|: \psi:\mathcal{D}\to\mathcal{D} \text{ holomorphic}, |\psi(0)|\le a\}$ is uniformly integrable on the unit circle. As an application, we derive a simple proof of the fact that, if $f$ is outer and $\phi:\mathcal{D}\to\mathcal{D}$ is holomorphic, then $f\circ\phi$ is outer.

On Symmetric Spaces With Convergence in Measure on Reflexive Subspaces

A closed subspace H of a symmetric space X on [0, 1] is said to be strongly embedded in X if in H the convergence in X-norm is equivalent to the convergence in measure. We study symmetric spaces X with the property that all their reflexive subspaces are strongly embedded in X. We prove that it is the case for all spaces, which satisfy an analogue of the classical Dunford–Pettis theorem on relatively weakly compact subsets in L1. At the same time the converse assertion fails for a broad class of separableMarcinkiewicz spaces.

Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications

In this paper, we present the $$L_p$$ convergence for partial sums $$S_n=\sum _{k=1}^nX_k$$ under the Cesaro uniform integrability condition and the complete convergence for the maximum of $$S_n$$ for sequences of widely orthant dependent random variables $$\{X_n,n\ge 1\}.$$ Some of the results extend the corresponding ones in reference. As applications, we get the complete consistency and the strong consistency for the estimator in a nonparametric regression model.

A Solution for the Uniform Integration of Field Devices in an Industrial Supervisory Control and Data Acquisition System

Supervisory Control and Data Acquisition (SCADA) systems are increasingly used solutions for monitoring and controlling various industrial processes. The existence of a large number of communication protocols helps to deploy complex systems that enable users to access data from one or more processes at a certain distance, and even control those processes. This article presents a solution for the uniform integration of field devices in an industrial SCADA system. This uniform integration is based on the CANopen communication protocol and the EDS files containing detailed descriptions of devices in a CANopen network. Based on the information and structure of the EDS files, we have designed and developed a database aimed at storing these data in an organization that enables them to be safely and efficiently processed. This database is the basis of a website application that enables the user to learn the characteristics of the field devices connected to the local industrial networks in a SCADA system.

On Balder’s Existence Theorem for Infinite-Horizon Optimal Control Problems

Balder’s well-known existence theorem (1983) for infinite-horizon optimal control problems is extended to the case in which the integral functional is understood as an improper integral. Simultaneously, the condition of strong uniform integrability (over all admissible controls and trajectories) of the positive part max{f0, 0} of the utility function (integrand) f0 is relaxed to the requirement that the integrals of f0 over intervals [T, T′] be uniformly bounded above by a function ω(T, T′) such that ω(T, T′) → 0 as T, T′→∞. This requirement was proposed by A.V. Dmitruk and N.V. Kuz’kina (2005); however, the proof in the present paper does not follow their scheme, but is instead derived in a rather simple way from the auxiliary results of Balder himself. An illustrative example is also given.

Laminated graphene oxide-supported high-efficiency microwave absorber fabricated by an in situ growth approach

Hydrotalcite-like CoFeAl-layered double hydroxide sheets (CoFeAl-LDH) are employed to construct the CoFeAl-LDH/G hybrids via the sufficient metal ions absorption and subsequent in-situ growth on graphene oxide (GO) surfaces. The uniform integration not only retains the inherent excellent properties of GO, but also overcomes some weakness like shallow skin depth and severe layers restack. In addition, extra dipolar polarization (induced by donated electron from GO) and Maxwell-Wagner-Sillars (MWS) effect (caused by abundant charges accumulation at the interfaces) also contribute to the remarkable microwave absorption performance. The maximum RL value and the effective bandwidth reach −23.8267 dB and 7.36 GHz, respectively at 2.5 mm. Consequently, study of structure-performance relationship is meaningful for the design and fabrication of binary absorbers with effective microwave absorption.

Integrated quantile functions: properties and applications

In this paper we provide a systematic exposition of basic properties of integrated distribution and quantile functions. We define these transforms in such a way that they characterize any probability distribution on the real line and are Fenchel conjugates of each other. We show that uniform integrability, weak convergence and tightness admit a convenient characterization in terms of integrated quantile functions. As an application we demonstrate how some basic results of the theory of comparison of binary statistical experiments can be deduced using integrated quantile functions. Finally, we extend the area of application of the Chacon--Walsh construction in the Skorokhod embedding problem.

TARGETED SEQUENTIAL DESIGN FOR TARGETED LEARNING INFERENCE OF THE OPTIMAL TREATMENT RULE AND ITS MEAN REWARD.

This article studies the targeted sequential inference of an optimal treatment rule (TR) and its mean reward in the non-exceptional case, i.e., assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adaptive statistical parameter is worthy of interest on its own. Our main result is a central limit theorem which enables the construction of confidence intervals on both mean rewards under the current estimate of the optimal TR and under the optimal TR itself. The asymptotic variance of the estimator takes the form of the variance of an efficient influence curve at a limiting distribution, allowing to discuss the efficiency of inference. As a by product, we also derive confidence intervals on two cumulated pseudo-regrets, a key notion in the study of bandits problems. A simulation study illustrates the procedure. One of the corner-stones of the theoretical study is a new maximal inequality for martingales with respect to the uniform entropy integral.

The \( L_r \) convergence and weak laws of large numbers for \(\widetilde{\rho}\)-mixing random variables

The \(L_{r}\) convergence and a class of weak laws of large numbers are obtained for sequences of \(\widetilde{\rho}\)-mixing random variables under the uniform CesA ro-type condition. This is weaker than the \(p\)th-order CesA ro uniform integrability. doi:10.1017/S1446181117000037

Preliminary studies of PVA/PVP blends incorporated with HAp and β-TCP bone ceramic as template for hard tissue engineering.

Polyvinylalcohol (PVA) and Polyvinylpyrrolidone (PVP) blend incorporated with hydroxyapatite (HAp) and β-tricalcium phosphate (β-TCP) is electrospun as nanofibrous composite scaffolds to act as suitable template for bone tissue engineering. Microscopic and spectroscopic characterizations confirm uniform integration of the crystalline calcium phosphate ceramics in the scaffolds. PVA-PVP blends are usually amorphous in nature and addition of phosphate ceramic particles specifically HAp elevates its crystalline behavior which is substantiated by XRD details. Further incorporation of ceramics is confirmed using FT-IR as characteristic PO43- groups for HAp and β-TCP were observed in the distinguished composites. Single glass transition temperature is observed for pure and composite blends indicating the formation of highly miscible blends. Also, addition of these ceramics augments the thermal stability of the blend scaffolds. Biocompatibility of the prepared (PVA: PVP)-HAp and (PVA: PVP)-TCP scaffolds is assessed using MG-63 Osteoblast cell lines in the time interval of 1st, 4th and 7th day. The cell viability percentage for (PVA: PVP)-HAp is high compared to β-TCP added blend composites, reinforcing the fact that scaffolds with good mechanical strength and enhanced porosity supports better cell adhesion.